Question

How many sides does a regular polygon have if the measure of each of its interior angle is 140

Answer 1

SOLUTION 1 : Find using interior angle:

Sum of all interior angles = (n - 2) x 180 where n is the number of sides

Find the number of sides:

140n = (n - 2) x 180

140n = 180n - 360

180n - 140n = 360

40n = 360

n = 360 ÷ 40 = 9

Answer: The polygon has 9 sides.

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SOLUTION 2: Find using exterior angle:

Interior angle = 140º

Find the exterior angle:

Interior angle + exterior angle = 180º

exterior angle = 180 - 140 = 40º

Find the number of sides:

Sum of exterior angles in any polygon is 360º

Number of sides = 360 ÷ 40 = 9

Answer: The polygon has 9 sides.

Answer 2

Answer:

9 sides

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